STATE SPACE POINT DISTRIBUTION PARAMETER FOR SUPPORT VECTOR MACHINE BASED CV UNIT CLASSIFICATION

Natarajan Meghanathan, et al. (Eds): ITCS, SIP, JSE-2012, CS & IT 04, pp. 291–302, 2012.
© CS & IT-CSCP 2012 DOI : 10.5121/csit.2012.2127
STATE SPACE POINT DISTRIBUTION
PARAMETER FOR SUPPORT VECTOR MACHINE
BASED CV UNIT CLASSIFICATION
N K Narayanan1
T M Thasleema 2
and V Kabeer3
1,2
Department of Information Technology, Kannur University, Kerala,
India,670567
1
nknarayanan@gmail.com, 2
thasnitm1@hotmail.com
3
Deaprtment of Computer Science, Farook College, University of Calicut
vkabeer@gmail.com
ABSTRACT
In this paper we extend Support Vector Machines (SVM) for speaker independent Consonant –
Vowel (CV) unit classification. Here we adopt the technique known as Decision Directed Acyclic
Graph (DDAG) , which is used to combine many two class classifiers into multiclass classifier.
Using Reconstructed State Space (RSS) based State Space Point Distribution (SSPD) parameters,
we obtain an average speaker independent phoneme recognition accuracy of 90% on the
Malayalam V/CV speech unit database. The recognition results indicate that this method is
efficient and can be adopted for developing a complete speech recognition system for Malayalam
language.
KEYWORDS
Reconstructed State Space, State Space Map, State Space Point Distribution Parameter, Support
Vector Machine
1. INTRODUCTION
In recent years Support Vector Machines (SVMs) have received significant attention because of
their excellent performance in pattern recognition applications [1] [2] [3] [4] [5]. It has the inbuilt
ability to solve pattern classification problem in a manner close to the optimum for the problem of
interest. Furthermore, SVM has the ability to achieve remarkable performance without prior
knowledge built into the design of the system. For the present study we make use this SVM
characteristics with time domain non-linear feature parameter namely State Space Point
Distribution (SSPD) for improving the recognition accuracies for Malayalam CV unit
classifications.
Recently emerged speech recognition systems use frequency-domain based traditional basic
speech features such as Linear Predictive Coding Coefficients (LPCC) and Mel Frequency
Cepstral Coefficients (MFCC), which are switched linear model of the human speech production
mechanism. One limitation of these models is the inability to extract the non-linear and higher-
order characteristics of the speech production process. Researchers in this area have already
suggested in literature that there is affirmation on non-linear characteristics in both voiced and

292 Computer Science & Information Technology (CS & IT)
unvoiced speech patterns [6][7][8]. To capture this non-linear information of Malayalam
Consonant CV speech unit, we introduce Reconstructed State Space (RSS) based State Space
Point Distribution (SSPD) parameters. P Prajith has presented RSS approach to prove the non-
linear and chaotic nature of the Malayalam vowels [9]. N K Narayanan & V Kabeer has proposed
State Space Map (SSM) and SSPD of the gray scale images for the computer recognition of
human faces and has got better recognition accuracy [10]. V L Lajish studied SSPD parameters
derived from the gray scale based SSMs of Malayalam handwritten character samples and
effectively utilized for high speed Handwritten Character Recognition (HCR) applications [11].
In the proposed work we use SSPD feature parameters for SVM based for Malayalam CV unit
classification.
A consonant can be defined as a unit sound in spoken language which are described by a
constriction or closure at one or more points along the vocal tract. According to Peter Ladefoged,
consonants are just ways of beginning or ending vowels [12]. Consonants are made by restricting
or blocking the airflow in some way and each consonant can be distinguished by place (where the
restriction is made) and manner (how the restriction is made) of articulation of a consonant. The
combination of place and manner of articulation is sufficient to uniquely identify a consonant
[13].
There have been a lot of well known attempts are reported in the literature towards automatic
speech recognition of V/CV speech units which kept the research in this area effective and
vibrant. Some of them are Mel Frequency Cepstral Coefficients (MFCC), Discrete Cosine
Transform (DCT), Formant Transition Information (FTI), Root Mean Square (RMS), Maximum
Amplitude (MA) and Zero Crossing Rates (ZCR), Expectation Maximization (EM) algorithm,
Variational Bayesian Principal Component Analyzers (VBPCA) to analyze mel frequency band
energies and obtain proper transformations, Reconstructed State Space (RSS) approach,
combination of RSS with MFCC, Discrete Wavelet Transform (DWT), Radial Basis Functions,
Self Organizing Maps and Time Delay Neural Networks(TDNN)[14][15][16]. Anitha et al had
proposed the methods for classification of multidimensional trajectories using Multiple
Outerproduct Matrices (MOM) method and studied their performance on recognition of spoken
letters using Support Vector Machines (SVMs) [17].
In the present study the recognition experiments are performed for 36 Malayalam consonants
using Malayalam CV speech unit database uttered by 96 different speakers. For the experimental
study, database is divided into five different phonetic classes based on the manner of articulation
of the consonants and are given by,
Table 1: Malayalam CV unit classes
Class Sounds
Unspirated /ka/, /ga/, /cha/, /ja/, /ta/, /da/, /tha/, /dha/, /pa/,/ba/
Aspirated /kha/,/gha/,/chcha/,/jha/, /tta/, /dda/, /ththa/, /dha/,/pha/, /bha/
Nasals /nga/,/na/,/nna/,/na/,/ma/
Approximants /ya/,/zha/,/va/,/lha/,/la/
Fricatives /sha/,/shsha/,/sa/,/ha/,/ra/,/rha/
This paper is organized as follows. Section 2 of this paper gives a detailed overview on RSS of
speech recognition. Section 3 gives the detailed description of SSM method. In section 4 SSPD
based feature extraction of the Malayalam CV speech unit is explained. Section 5 describes
classification using SVM classifier. Section 6 presents the simulation experiment conducted using
Malayalam CV speech unit database and reports the recognition results obtained using SVM
classifier. Finally section 7 gives the conclusion and direction for future work.

Computer Science & Information Technology (CS & IT) 293
2. RECONSTRUCTED STATE SPACE FOR SPEECH RECOGNITION
In dynamical system approach, by embedding a signal into adequately high dimensional space, a
topologically equivalent to the original state space structure of the system generating the signal is
formed [18][19]. This embedding is known as Reconstructed State Space (RSS), is typically
constructed by mapping time-lagged copies of the original signal onto axes of the new high
dimensional space. The time evolution within the RSS traces out a trajectory pattern referred to as
its attractor which is a representation of the dynamics of the underlying system [20]. Since the
attractor of an RSS captures all the relevant information about the underlying system, it is an
efficient choice for signal analysis, processing and classifications. Sheikh Zadeh and Deng has
proposed a work in time domain representation of speech signal using autoregressive modelling
[21]. The RSS approach proposed here has the advantage of extracting both linear and non-linear
aspects of the entire system.
Takens’ theorem states that under certain assumptions, state space of a dynamical system can be
constructed through the use of time delayed versions of the original scalar measurements [22].
Thus a RSS can be considered as a powerful tool for signal processing domain in non-linear or
even chaotic dynamical systems [23][24]. According to Takens embedding theorem, a RSS for a
dynamical system can be produced for a measured state variable Sn, n=1,2,3,…..N via method of
delays by creating vectors given by
sn = [sn sn+τ sn+2τ ……… sn+(d-1)τ]-------------------(1)
where d is the embedding dimension and τ is the time delay value. The row vector sn defines the
position of a single point in the RSS. To completely define the dynamics of the system and to
create a d dimensional RSS, corresponding trajectory matrix is given as
Sd














=
−++
−++
−++
ττ
ττ
ττ
)1(
)1(222
)1(111
...
............
...
...
dNNN
d
d
sss
sss
sss
-----------------------(2)
A speech signal with amplitude values can be treated as a dynamical system with one
dimensional time series data. Based on the above theory, this study investigates a method to
model a RSS for Malayalam consonants through the use of time delayed versions of original
scalar measurements. Thus a trajectory matrix S1 with embedding dimension d=2 and τ=1 can be
constructed by considering the speech amplitude values sn as one dimensional time series data.
Thus S1 is given as
S1












=
− NN s
s
s
s
s
s
......
3
2
1
2
1
------------------------(3)
The concept of time delay embedding was first introduced by Packard et al based on the theorem
by Whitney related to topological embeddings in Cartesian Spaces [25][26]. From this idea
Takens proved an important theoretical justification for the practical use of time delay
reconstructions.

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
RSS plot for the sound /ka/
Figure 1: RSS plot for the Sound /ka/ with d=2.
3. STATE SPACE MAP FOR THE SPEECH RECOGNITION
The State Space Map (SSM) in two dimension for the Malayalam consonant CV unit is
constructed as follows. The normalized N samples values for each CV unit is the scalar time
series sn where n=1,2,3……N. For every consonant speech signal a trajectory matrix is formed
with embedding dimension d=2 and time delay τ=1. Now the scatter plot SSM is generated by
plotting the row values of the above constructed trajectory matrix by plotting sn versus sn+1.
Figure 2 shows the SSM for the first consonant sound /ka/.
-1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-1
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Sn
Sn+1
SSM for the sound /ka/
Figure 2. Scatter plot for the sound /ka/ with d=2
4. STATE SPACE POINT DISTRIBUTION FEATURES FROM STATE SPACE
MAP
In Automatic Speech Recognition (ASR), selection of distinctive features is certainly the most
important factor for the high recognition performance. Present study uses non linear feature
extraction technique called State Space Point Distribution (SSPD) from their SSM. For this
purpose the SSM of the speech unit is divided into grids with 20 X 20 boxes. The box defined by
co-ordinates (-1,0.9),(-0.9,1) is taken as box 1 and box just right side to it as taken as box 2 and so
on in the x-direction with the last box being (0.9,0.9),(1,1) is taken as box 20. The process is
repeated for all the rows and boxes are numbered consecutively for the 400 boxes. The SSPD for
each pattern is calculated by estimating the number of points distributed in each of these 400
boxes. This can be mathematically represented as follows.

The reconstructed SSPD parameter for location ‘i’ in two dimensions can be defined as
( ) ∑=
+=
N
n
nni issfSSPD
1
1 )],,([ ----------------------------(3)
where =+ )]),,([ 1 issf nn 1, if state space point defined by the row vector ],[ 1+nn ss is in the
location ‘i’
0, otherwise
More generally reconstructed SSPD parameter for location ‘i’ in d dimension can be defined as
∑=
−+++=
N
n
dnnnni issssfSSPD
1
)1(2 )],.,.........,,([)( τττ ------------------------(4)
where )],.,.........,,([ )1(2 issssf dnnnn τττ −+++ =1, if state space point defined by the row vector
].,.........,,[ )1(2 τττ −+++ dnnnn ssss is in the location ‘i’
0, otherwise.
Using this information the SSPD plot is plotted by taking the box number along x-axis and the
number of points in each box along y-axis. The SSPD plot for the first Malayalam CV sound /ka/
is given in figure 3.
0 50 100 150 200 250 300 350 400
0
50
100
150
200
250
300
350
400
450
Location Number
Numberofpoints
Figure 3: SSPD plot for the sound /ka/
The SSM and the corresponding SSPD plot obtained for different speaker shows the identity of
the sound so that an efficient feature vector can be formed using SSPD. The feature vector of size
20 is estimated by taking the average distribution of each row in the SSPD graph. Figure 4 shown
below describe the feature vector extracted for 10 different speakers for the Malayalam CV unit
/ka/. The graph obtained for different sounds seems to be distinguishable.

0 2 4 6 8 10 12 14 16 18 20
0
10
20
30
40
50
60
70
80
Feature Number
SSPDFeatureValue
Figure 4 : Feature vector plot plotted for 10 samples of the first speech sound /ka/
5. CLASSIFICATION USING SUPPORT VECTOR MACHINES
Pattern recognition can be defined as a field concerned with machine recognition of meaningful
regularities in noisy or complex environments [27]. Nowadays pattern recognition is an integral
part of most intelligent systems built for decision making. In the present study widely used
approaches for pattern recognition problems namely connectionist approaches (ANN) is used.
The task of a classifier component proper of a full system is to use the feature vector provided by
the feature extractor to assign the object to a category [28].
SVM is a linear machine with some specific properties. The basic principle of SVM in pattern
recognition application is to build an optimal separating hyperplane in such a way to separate two
classes of pattern with maximal margin [29]. SVM accomplish this desirable property based on
the idea of Structural Risk Minimization (SRM) from statistical learning theory which shows that
the error rate of a learning machine on test data (i.e generalization error report ) is bounded by the
sum of training error rate and the term that depending on the Vapnik – Chervonenkis (VC)
dimension of the learning system [30][31]. By minimizing this upper bound high generalization
performance can be obtained. For separable patterns SVM produces a value of 0 for first term and
minimizes the second term. Furthermore, SVMs are quite different from other machine learning
techniques in generalization of errors which are not related to the input dimensionality of the
problem, but to the margin with which it separates data. This is the reason why SVMs can have
good performance even in large number of input problems [32] [33].
SVMs are mainly used for binary classifications. For combining the binary classification into
multiclass classification a relatively new learning architecture namely Decision Directed Acyclic
Graph (DDAG) is used. For N class problem, the DDAG contains, one for each pair of classes.
DDAGSVM works in a kernel induced feature space and uses two class maximal margin
hyperplane at each decision node of the DDAG. The DDAGSVM is considerably faster to train
and evaluate comparable to other algorithms.
The present study proposes an SVM based recognition system for Malayalam CV speech unit
recognition. The support vectors consist of small subset of training data extracted by the
DDAGSVM algorithm. The simulation experiment and the results obtained using SVM approach
is explained in the next section.

6. SIMULATION EXPERIMENT AND RESULTS
All the simulation experiments are carried out using Malayalam CV speech unit database, uttered
by 96 different speakers. We used 8 kHz sampled speech signal which is low pass filtered to band
limit to 4 kHz.
As explained in Section 2 an example of RSS plot with dimension 2 and time delay 1 taken from
the Malayalam CV speech database for five different phonetic classes of aspirated, un aspirated,
nasals, approximants and fricatives are given in figure 4(a-e). A visual representation of system
dynamics are evident from this plot.
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
RSS Plot for the sound /ka/
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
RSS plot for the sound /kha/
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
RSS plot for sound /nga/
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
RSS plot for the sound /ya/
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
RSS Plot for sound /sha/
Figure 4: RSS Plot for the sounds (a)/ka/ (b) /kha/ (c) /nga/ (d) /ya/ (e) /ra/ from 5 different classes
Using this RSS plot, reconstructed state space distribution (scatter diagram) or SSM plot in two
dimension is constructed for each of these five different phonetic classes are shown in figure 5(a-
e).
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Sn
Sn+1
SSM for group 1
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Sn
Sn+1
SSM for group (5)
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Sn
Sn+1
SSM for group(2)
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Sn
Sn+1
SSM for group (3)
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Sn
Sn+1
SSM for group (4)
Figure 5:SSM plot for 5 classes
As explained in Section 4 we have modelled and characterized each CV speech signal using
SSPD plot derived from SSM plot. Thus the non – linear SSPD parameters are extracted based on
SSPD plot. Figure 6 shows SSPD plot of 6 instances of the same sound to analyze the efficiency
of this method.

0 50 100 150 200 250 300 350 400
0
100
200
300
400
500
600
700
800
900
Location Number
NumberofPoints
SSPD for sound /ka/ speaker (1)
0 50 100 150 200 250 300 350 400
0
100
200
300
400
500
600
700
Location Number
NumberofPoints
SSPD for /ka/ Speaker (3)
0 50 100 150 200 250 300 350 400
0
200
400
600
800
1000
1200
Location Number
NumberofPoints
0 50 100 150 200 250 300 350 400
0
100
200
300
400
500
600
700
800
900
1000
Location Number
NumberofPoints
SSPD for /ka/ speaker (4)
0 50 100 150 200 250 300 350 400
0
100
200
300
400
500
600
700
Location Number
NumberofPoints
0 50 100 150 200 250 300 350 400
0
100
200
300
400
500
600
700
800
900
Location Number
NumberofPoints
Figure 6:SSPD plot of first 6 instance of the sound /ka/ of different speakers
Observation on these graphs revels that structure of point distribution are very similar and hence
they represent the same CV speech unit. Again figure 7 shows SSPD graph of 5 different sounds
from 5 different phonetic classes of the Malayalam CV speech database of the same speaker.
0 50 100 150 200 250 300 350 400
0
50
100
150
200
250
300
350
400
450
Location Number
NumberofPoints
SSPD plot for group(1)
0 50 100 150 200 250 300 350 400
0
200
400
600
800
1000
1200
Location Number
NumberofPoints
SSPD plot for group(2)
0000 50505050 100100100100 150150150150 200200200200 250250250250 300300300300 350350350350 400400400400
0000
200200200200
400400400400
600600600600
800800800800
1000100010001000
1200120012001200
Location Number
Numberofpoints
SSPD Plot for Group(3)
0 50 100 150 200 250 300 350 400
0
100
200
300
400
500
600
700
800
SSPD for Group(4)
Location Number
NumberofPoints
0 50 100 150 200 250 300 350 400
0
50
100
150
200
250
300
350
400
450
500
Location Number
NumberofPoints
SSPD for Group (5)
Figure 7: SSPD plot for 5 different classes of same speaker
Considerable change in the SSPD plot structure shows the difference in sound class or group
under classification. Hence the SSPD feature vectors can effectively used for the classification
purpose. Classifications are done using SVM classifier.

The classification is conducted for 36 Malayalam CV speech unit using Malayalam CV speech
database uttered by 96 different speakers. We divide the dataset into training and test set which
contains first 48 samples for training and next 48 for testing. Thus training and test set contains
total of 1728 samples each. The experimental study by grouping the Malayalam CV speech
database into five different phonetic classes are presented and tabulated in table 3. The
classification result is obtained an average of 90.07% using Support Vector Machine. Table 2
gives comparative study of V/CV unit speech recognition results of other methods in literature
with the present work using TIMIT speech database. The method denoted with * indicates for
Malayalam CV database. Table 3 shows that the proposed methods yields a good or comparable
result.
Table 2: Some popular methods and their results
Sl No Method Accuracy (%)
1 DWT+RBF 36.3
2 DWT+SOM 46.7
3 RSS 49.56
4 RSS+MFCC 65.68
5 ZCR* 73.8
6 EM 58.7
7 VBPCA 59.6
Table 3: Experimental results using SSPD features of 5 classes
Class Recognition Accuracy
Using SVM
Unaspirated 84.15
Aspirated 83.63
Nasals 96.23
Approximants 94.92
Fricatives 91.43
Average 90.07
7. CONCLUSIONS
This paper proposes Decision Directed Acyclic Graph (DDAG) algorithm for Malayalam CV
speech unit recognition using Support Vector Machines (SVMs). A novel and accurate feature
extraction technique using statistical models of Reconstructed State Space (RSS) has been
studied. The State Space Map (SSM) and State Space Point Distribution (SSPD) plots for each
speech unit are drawn. Finally a feature vector named SSPD parameter of size 20 is formed. The
recognition accuracies are calculated using DDAGSVM algorithm. Experimental results are
reported to illustrate the effectiveness and robustness of the proposed method. More effective
implementation of RSS features in combination with frequency domain features and the
development of multistage classifiers would be some of our future research work.

REFERENCES
[1] V.N. Vapnik, (1995) The Nature of Statistical Learning Theory, New York, Springer Verlag,
[2] B.E. Boser, I.M. Guyon, and V.N. Vapnik,(1995) “A Training Algorithm for Optimal Margin
Classifiers,” Proc. Fifth Ann.Workshop Computing Learning Theory, pp. 144-15.
[3] V.N. Vapnik, (1999) “An Overview of Statistical Learning Theory,” IEEE Trans. Neural Networks,
vol. 10, no. 5, pp. 988-999.
[4] C. Cortes and V.N. Vapnik,(1995) “Support-Vector Networks,” Machine Learning, vol. 20, pp. 273-
297.
[5] B. Scholkopf, (1997) “Support Vector Learning,” PhD dissertation, Technische Universitat Berlin,
Germany, 1997.
[6] M. Banbrook and S. McLaughlin,(1994) “Is Speech Chaotic?,” in Proc. IEE Colloq. Exploiting
Chaos in Signal Processing, pp.1– 8, 1994.
[7] M. Casdagli, (1991) “Chaos and Deterministic Versus Stochastic Nonlinear Modeling,” J. R. Statist.
Soc. B, vol. 54, pp. 303–328.
[8] H. M. Teager and S. M. Teager,(1990) “Evidence for Nonlinear Sound Production Mechanisms in the
Vocal Tract,” in Proc.NATO ASI Speech Production Speech Modeling, pp. 241–261
[9] P Prajith,(2008) Investigations on the Applications of Dynamical Instabilities and Deterministic
Chaos for Speech Signal Processing, PhD Thesis, Department of Physics, University of Calicut.
[10] N K Narayanan and V kabeer, “Face Recognition using Non-linear Feature Parameter and Artificial
Neural Network”, International Journal of Computational Intelligent Systems, Vol 3. No. 5, pp. 566 –
574.
[11] V L Lajish, (2007) Adaptive neuro – Fuzzy Inference Based Pattern Recognition Studies on
Handwritten Character Images, PhD Thesis, University of Calicut.
[12] Peter Ladefoged,(2004 Vowels and Consonants- an Introduction to the Sounds of Language,
BlackWell Publishing.
[13] Danial Jurafsky, James H Martin,(2004) An Introduction to Natural Language Processing,
Computational Linguistics, and Speech Recognition, Pearson Educatio.
[14] Oh – Wook Kwon, Kwowlecing Chcn and Te – Won Lee, “Speech Feature Analysis using
Variatioanl Bayesian PCA”, IEEE Signal Proc. Letters, Vol. 10(5), 2003.
[15] Samouelian A, “Knowledge based Approach to Consonant Recognition”, IEEE international Conf. on
ASSP, pp. 77 – 80, 1994.
[16] Cutajar M, Gatt E, Grech I, Casha O and Micallef J, “Neural Network Architectures for Speaker
Independent Phoneme Recognition”, 7th International Symposium on Image and Signal Processing
Analysis, Croatia, pp. 90 – 95, 2011.
[17] R Anitha, D Srikrishna Satish and C Chandra Shekhar, “Outerproduct of Trajectory matrix for
Acoustic Modelling using Support Vector Machines”, IEEE Workshop on Machine Learning for
Signal Processing, pp. 355 – 363, 2004.
[18] E. Ott,(1993) Chaos in Dynamical Systems, Cambridge University Press.
[19] G. L. Baker and J Gollub, (1996) Chaotic Dynamics : An Introduction, Cambridge University Press.

[20] Michael T Jhonson, Rchard J Povinalli, Andrew C Lindgren, Jinjin Ye, Xiaolin Liu and Kevin
Indrebo, (2005), “Time Domain Isolated Phoneme Classification using Reconstructed Phase Space”,
IEEE Trans. On Speech and Audio Processing, Vol.13, No. 4, pp. 458 – 466.
[21] H. Sheikhzadeh and L. Deng, (1994) “Waveform-based Speech Recognition Using Hidden Filter
Models: Parameter Selection and Sensitivity to Power Normalization,” IEEE Trans. Acoust., Speech,
Signal Processing, vol. 2, pp. 80–91.
[22] F. Takens, (1980), ”Detecting Strange Attractors in Turbulence”, in Proc. Dynamical Systems and
Turbulence, Warwick, U.K., pp. 366–381.
[23] H. Kantz and T. Schreiber, (1997) Non Linear Time Series Analysis, Cambridge University Press.
[24] D. S. Broomhead and G. P. King, (1986) “Extracting qualitative Dynamics from experimental data”,
Physica D, pp 217 – 236.
[25] N. H. Packard, J. P. Crutchfield, J. D. Farmer, and R. S. Shaw,(1980) “Geometry from a time series,”
Phys. Rev. Lett., vol. 45, pp. 712–716.
[26] H. Whitney,(1936) “Differentiable manifolds,” Ann. Math., ser. 2nd, vol. 37,pp. 645–680.
[27] Duda . R. O and Hart P. E,(1973) Pattern Classification and Scene Analysis, Wiley Inter cience, New
York.
[28] Duda R O, Hart P E and David G. Stork,(2006) Pattern Classification, A Wiley-Inter Science
Publications.
[29] Ying Tan and Jun Wang, (2004), “A Support Vector Machine with a Hybrid Kernel and Minimal
Vapnik – Chervonenkins Dimension”, IEEE Trans. On Knowledge and Data Engineering, Vol. 10,
No. 4, pp. 385 – 395 .
[30] Vladimir N Vapnik, (1999), “An Overview of Statistical Learning Theory”, IEEE Trans. On Neural
Networks, Vol. 10, No. 5, pp. 988 – 999 .
[31] Ravi Gupta, Ankush Mittal and Kuldip Singh, “A time Series based Feature Extraction Approach for
Prediction of Protein Structured Class”, EURASIP Journal on Bioinformatics and System Biology,
2008.
[32] E. Osuna, R. Freund, and F. Girosi,(1997) “Training Support Vector Machines: An Application to
Face Detection,” Proc. IEEE Conf.Computer Vision and Pattern Recognition, pp. 17-19.
[33] M. Pontil and A. Verri,(1998), “Support Vector Machines for 3D Object Recognition,” IEEE Trans.
Pattern Analysis and Machine Intelligence, vol. 20, no. 6, pp. 637-646.

Authors
Dr. N.K. Narayanan is a Senior Professor of Information Technology, Kannur University,
Karala, India. He earned a Ph.D in speech signal processing from Department of
Electronics, CUSAT, Kerala, India in 1990. He has published about eighty four research
papers in national & international journals in the area of Speech processing, Image
processing, Neural networks, ANC and Bioinformatics. He has served as Chairman of the
School of Information Science & Technology, Kannur University during 2003 to 2008,
and as Principal, Coop Engineering College, Vadakara, Kerala, India during 2009-10. Currently he is the
Director, UGC IQAC, Kannur University.
T M Thasleema had her M Sc in Computer Science from Kannur University, Kerala, India
in 2004. She had to her credit one book chapter and many research publications in national
and international levels in the area of speech processing and pattern recognition. Currently
she is doing her Ph.D in speech signal processing at Department of Information
Technology, Kannur University under the supervision of Prof Dr N. K Narayanan.
Dr. Kabeer V. is the head of the Postgraduate Department of Computer Science, Farook
College, Kozhikode, Kerala, India, since July 2011. Previously, he was Associate
Professor at MES College of Engineering, Kuttippuram, Kerala, India. He earned his Ph.D.
from the Department of Information Technology, Kannur University under the supervision
of Prof. Dr. N.K. Narayanan. His research interests include but not limited to Face
Recognition, Image Processing, Fuzzy Logic etc. He is a life member of Indian Society for
Technical Education, India.

STATE SPACE POINT DISTRIBUTION PARAMETER FOR SUPPORT VECTOR MACHINE BASED CV UNIT CLASSIFICATION

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Similar to STATE SPACE POINT DISTRIBUTION PARAMETER FOR SUPPORT VECTOR MACHINE BASED CV UNIT CLASSIFICATION

Similar to STATE SPACE POINT DISTRIBUTION PARAMETER FOR SUPPORT VECTOR MACHINE BASED CV UNIT CLASSIFICATION (20)

More from cscpconf

More from cscpconf (20)

Recently uploaded

Recently uploaded (20)

STATE SPACE POINT DISTRIBUTION PARAMETER FOR SUPPORT VECTOR MACHINE BASED CV UNIT CLASSIFICATION